QuestionSimplify $(3.2)(3.2^2)^4$ . Choices: $(3.2)^9$ , $(3.2)^8$ , $(3.2)^7$ , $(3.2)^6$ .

Studdy Solution

STEP 1

Assumptions1. We are simplifying the expression $(3.)\left(3.^{}\right)^{4}$ . We will use the laws of exponents to simplify the expression

STEP 2

First, we need to simplify the expression inside the parentheses, $(.2^{2})^{4}$ . According to the power of a power rule, when you raise a power to a power, you multiply the exponents.
$(a^{m})^{n} = a^{m \times n}$

STEP 3

Now, plug in the given values for $a$ , $m$ , and $n$ to calculate the simplified expression.
$(3.2^{2})^{} =3.2^{2 \times}$

STEP 4

Calculate the exponent.
$3.2^{2 \times4} =3.2^{8}$

STEP 5

Now, we need to multiply $3.2$ by $3.2^{8}$ . According to the product of powers rule, when you multiply powers with the same base, you add the exponents.
$a^{m} \times a^{n} = a^{m + n}$

STEP 6

Plug in the given values for $a$ , $m$ , and $n$ to calculate the simplified expression.
$3.2 \times3.2^{8} =3.2^{1 +8}$

STEP 7

Calculate the exponent.
$3.2^{1 +} =3.2^{9}$ So, the simplified expression is $(3.2)^{9}$ .

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QuestionSimplify $(3.2)(3.2^2)^4$ . Choices: $(3.2)^9$ , $(3.2)^8$ , $(3.2)^7$ , $(3.2)^6$ .

Studdy Solution

STEP 1

Assumptions1. We are simplifying the expression $(3.)\left(3.^{}\right)^{4}$ . We will use the laws of exponents to simplify the expression

STEP 2

First, we need to simplify the expression inside the parentheses, $(.2^{2})^{4}$ . According to the power of a power rule, when you raise a power to a power, you multiply the exponents.
$(a^{m})^{n} = a^{m \times n}$

STEP 3

Now, plug in the given values for $a$ , $m$ , and $n$ to calculate the simplified expression.
$(3.2^{2})^{} =3.2^{2 \times}$

STEP 4

Calculate the exponent.
$3.2^{2 \times4} =3.2^{8}$

STEP 5

Now, we need to multiply $3.2$ by $3.2^{8}$ . According to the product of powers rule, when you multiply powers with the same base, you add the exponents.
$a^{m} \times a^{n} = a^{m + n}$

STEP 6

Plug in the given values for $a$ , $m$ , and $n$ to calculate the simplified expression.
$3.2 \times3.2^{8} =3.2^{1 +8}$

STEP 7

Calculate the exponent.
$3.2^{1 +} =3.2^{9}$ So, the simplified expression is $(3.2)^{9}$ .

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QuestionSimplify (3.2)(3.22)4(3.2)(3.2^2)^4(3.2)(3.22)4. Choices: (3.2)9(3.2)^9(3.2)9, (3.2)8(3.2)^8(3.2)8, (3.2)7(3.2)^7(3.2)7, (3.2)6(3.2)^6(3.2)6.

Studdy Solution

STEP 1

Assumptions1. We are simplifying the expression (3.)(3.)4(3.)\left(3.^{}\right)^{4}(3.)(3.)4 . We will use the laws of exponents to simplify the expression

STEP 2

First, we need to simplify the expression inside the parentheses, (.22)4(.2^{2})^{4}(.22)4. According to the power of a power rule, when you raise a power to a power, you multiply the exponents.(am)n=am×n(a^{m})^{n} = a^{m \times n}(am)n=am×n

STEP 3

Now, plug in the given values for aaa, mmm, and nnn to calculate the simplified expression.(3.22)=3.22×(3.2^{2})^{} =3.2^{2 \times}(3.22)=3.22×

STEP 4

Calculate the exponent.3.22×4=3.283.2^{2 \times4} =3.2^{8}3.22×4=3.28

STEP 5

Now, we need to multiply 3.23.23.2 by 3.283.2^{8}3.28. According to the product of powers rule, when you multiply powers with the same base, you add the exponents.am×an=am+na^{m} \times a^{n} = a^{m + n}am×an=am+n

STEP 6

Plug in the given values for aaa, mmm, and nnn to calculate the simplified expression.3.2×3.28=3.21+83.2 \times3.2^{8} =3.2^{1 +8}3.2×3.28=3.21+8

STEP 7

Calculate the exponent.3.21+=3.293.2^{1 +} =3.2^{9}3.21+=3.29So, the simplified expression is (3.2)9(3.2)^{9}(3.2)9.

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QuestionSimplify $(3.2)(3.2^2)^4$ . Choices: $(3.2)^9$ , $(3.2)^8$ , $(3.2)^7$ , $(3.2)^6$ .

Assumptions1. We are simplifying the expression $(3.)\left(3.^{}\right)^{4}$ . We will use the laws of exponents to simplify the expression

First, we need to simplify the expression inside the parentheses, $(.2^{2})^{4}$ . According to the power of a power rule, when you raise a power to a power, you multiply the exponents.
$(a^{m})^{n} = a^{m \times n}$

Now, plug in the given values for $a$ , $m$ , and $n$ to calculate the simplified expression.
$(3.2^{2})^{} =3.2^{2 \times}$

Calculate the exponent.
$3.2^{2 \times4} =3.2^{8}$

Now, we need to multiply $3.2$ by $3.2^{8}$ . According to the product of powers rule, when you multiply powers with the same base, you add the exponents.
$a^{m} \times a^{n} = a^{m + n}$

Plug in the given values for $a$ , $m$ , and $n$ to calculate the simplified expression.
$3.2 \times3.2^{8} =3.2^{1 +8}$

Calculate the exponent.
$3.2^{1 +} =3.2^{9}$ So, the simplified expression is $(3.2)^{9}$ .