QuestionSimplify the following expressions:
1. $3^{8} \times 3^{4}=$
2. $8^{10} \times 8^{7}=$
3. $m^{5} \times m^{2}=$
4. $b^{12} \div b^{5}=$
5. $6^{12} \times 6^{6} \div 6^{8} \times 6^{2}=$
6. $c^{5} \times c^{4}=$

Studdy Solution

STEP 1

Assumptions1. The expressions are in the form of $a^{m} \times a^{n}$ or $a^{m} \div a^{n}$ , where $a$ is the base and $m$ and $n$ are the exponents. . The properties of exponents are used to simplify the expressions. Specifically, when multiplying like bases, we add the exponents, and when dividing like bases, we subtract the exponents.

STEP 2

To simplify the expression $^{8} \times^{4}$ , we add the exponents because the bases are the same and we are multiplying.
$^{8} \times^{4} =^{8+4}$

STEP 3

Calculate the sum of the exponents.
$3^{8} \times3^{} =3^{12}$

STEP 4

To simplify the expression $8^{10} \times8^{7}$ , we add the exponents because the bases are the same and we are multiplying.
$8^{10} \times8^{7} =8^{10+7}$

STEP 5

Calculate the sum of the exponents.
$8^{10} \times8^{7} =8^{17}$

STEP 6

To simplify the expression $m^{5} \times m^{2}$ , we add the exponents because the bases are the same and we are multiplying.
$m^{5} \times m^{2} = m^{5+2}$

STEP 7

Calculate the sum of the exponents.
$m^{5} \times m^{2} = m^{7}$

STEP 8

To simplify the expression $b^{12} \div b^{5}$ , we subtract the exponents because the bases are the same and we are dividing.
$b^{12} \div b^{5} = b^{12-5}$

STEP 9

Calculate the difference of the exponents.
$b^{12} \div b^{5} = b^{7}$

STEP 10

To simplify the expression $6^{12} \times6^{6} \div6^{8} \times6^{2}$ , we add the exponents of the terms we are multiplying and subtract the exponents of the terms we are dividing.
$6^{12} \times6^{6} \div6^{8} \times6^{2} =6^{12+6-8-2}$

STEP 11

Calculate the sum and difference of the exponents.
$6^{} \times6^{6} \div6^{8} \times6^{} =6^{8}$

STEP 12

To simplify the expression $c^{5} \times c^{4}$ , we add the exponents because the bases are the same and we are multiplying.
$c^{5} \times c^{4} = c^{5+4}$

STEP 13

Calculate the sum of the exponents.
$c^{5} \times c^{} = c^{9}$ So the simplified expressions are2. $3^{8} \times3^{}=3^{12}$
3. $8^{10} \times8^{7}=8^{17}$ . $m^{5} \times m^{2}=m^{7}$
5. $b^{12} \div b^{5}=b^{7}$
6. $6^{12} \times6^{6} \div6^{8} \times6^{2}=6^{8}$
7. $c^{5} \times c^{}=c^{9}$

Was this helpful?

QuestionSimplify the following expressions:
1. $3^{8} \times 3^{4}=$
2. $8^{10} \times 8^{7}=$
3. $m^{5} \times m^{2}=$
4. $b^{12} \div b^{5}=$
5. $6^{12} \times 6^{6} \div 6^{8} \times 6^{2}=$
6. $c^{5} \times c^{4}=$

Studdy Solution

STEP 1

STEP 2

To simplify the expression $^{8} \times^{4}$ , we add the exponents because the bases are the same and we are multiplying.
$^{8} \times^{4} =^{8+4}$

STEP 3

Calculate the sum of the exponents.
$3^{8} \times3^{} =3^{12}$

STEP 4

To simplify the expression $8^{10} \times8^{7}$ , we add the exponents because the bases are the same and we are multiplying.
$8^{10} \times8^{7} =8^{10+7}$

STEP 5

Calculate the sum of the exponents.
$8^{10} \times8^{7} =8^{17}$

STEP 6

To simplify the expression $m^{5} \times m^{2}$ , we add the exponents because the bases are the same and we are multiplying.
$m^{5} \times m^{2} = m^{5+2}$

STEP 7

Calculate the sum of the exponents.
$m^{5} \times m^{2} = m^{7}$

STEP 8

To simplify the expression $b^{12} \div b^{5}$ , we subtract the exponents because the bases are the same and we are dividing.
$b^{12} \div b^{5} = b^{12-5}$

STEP 9

Calculate the difference of the exponents.
$b^{12} \div b^{5} = b^{7}$

STEP 10

To simplify the expression $6^{12} \times6^{6} \div6^{8} \times6^{2}$ , we add the exponents of the terms we are multiplying and subtract the exponents of the terms we are dividing.
$6^{12} \times6^{6} \div6^{8} \times6^{2} =6^{12+6-8-2}$

STEP 11

Calculate the sum and difference of the exponents.
$6^{} \times6^{6} \div6^{8} \times6^{} =6^{8}$

STEP 12

To simplify the expression $c^{5} \times c^{4}$ , we add the exponents because the bases are the same and we are multiplying.
$c^{5} \times c^{4} = c^{5+4}$

STEP 13

Calculate the sum of the exponents.
$c^{5} \times c^{} = c^{9}$ So the simplified expressions are2. $3^{8} \times3^{}=3^{12}$
3. $8^{10} \times8^{7}=8^{17}$ . $m^{5} \times m^{2}=m^{7}$
5. $b^{12} \div b^{5}=b^{7}$
6. $6^{12} \times6^{6} \div6^{8} \times6^{2}=6^{8}$
7. $c^{5} \times c^{}=c^{9}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

To simplify the expression 8×4^{8} \times^{4}8×4, we add the exponents because the bases are the same and we are multiplying.8×4=8+4^{8} \times^{4} =^{8+4}8×4=8+4

STEP 3

Calculate the sum of the exponents.38×3=3123^{8} \times3^{} =3^{12}38×3=312

STEP 4

To simplify the expression 810×878^{10} \times8^{7}810×87, we add the exponents because the bases are the same and we are multiplying.810×87=810+78^{10} \times8^{7} =8^{10+7}810×87=810+7

STEP 5

Calculate the sum of the exponents.810×87=8178^{10} \times8^{7} =8^{17}810×87=817

STEP 6

To simplify the expression m5×m2m^{5} \times m^{2}m5×m2, we add the exponents because the bases are the same and we are multiplying.m5×m2=m5+2m^{5} \times m^{2} = m^{5+2}m5×m2=m5+2

STEP 7

Calculate the sum of the exponents.m5×m2=m7m^{5} \times m^{2} = m^{7}m5×m2=m7

STEP 8

To simplify the expression b12÷b5b^{12} \div b^{5}b12÷b5, we subtract the exponents because the bases are the same and we are dividing.b12÷b5=b12−5b^{12} \div b^{5} = b^{12-5}b12÷b5=b12−5

STEP 9

Calculate the difference of the exponents.b12÷b5=b7b^{12} \div b^{5} = b^{7}b12÷b5=b7

STEP 10

STEP 11

Calculate the sum and difference of the exponents.6×66÷68×6=686^{} \times6^{6} \div6^{8} \times6^{} =6^{8}6×66÷68×6=68

STEP 12

To simplify the expression c5×c4c^{5} \times c^{4}c5×c4, we add the exponents because the bases are the same and we are multiplying.c5×c4=c5+4c^{5} \times c^{4} = c^{5+4}c5×c4=c5+4

STEP 13

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

To simplify the expression $^{8} \times^{4}$ , we add the exponents because the bases are the same and we are multiplying.
$^{8} \times^{4} =^{8+4}$

Calculate the sum of the exponents.
$3^{8} \times3^{} =3^{12}$

To simplify the expression $8^{10} \times8^{7}$ , we add the exponents because the bases are the same and we are multiplying.
$8^{10} \times8^{7} =8^{10+7}$

Calculate the sum of the exponents.
$8^{10} \times8^{7} =8^{17}$

To simplify the expression $m^{5} \times m^{2}$ , we add the exponents because the bases are the same and we are multiplying.
$m^{5} \times m^{2} = m^{5+2}$

Calculate the sum of the exponents.
$m^{5} \times m^{2} = m^{7}$

To simplify the expression $b^{12} \div b^{5}$ , we subtract the exponents because the bases are the same and we are dividing.
$b^{12} \div b^{5} = b^{12-5}$

Calculate the difference of the exponents.
$b^{12} \div b^{5} = b^{7}$

Calculate the sum and difference of the exponents.
$6^{} \times6^{6} \div6^{8} \times6^{} =6^{8}$

To simplify the expression $c^{5} \times c^{4}$ , we add the exponents because the bases are the same and we are multiplying.
$c^{5} \times c^{4} = c^{5+4}$