QuestionSolve for the unknowns in the equation: $\frac{2 x^{4} y^{?} z^{-3}}{3 x^{?} y^{-3} z^{?}}=\frac{2 x^{2}}{3 y z^{7}}$ .

Studdy Solution

STEP 1

Assumptions1. We assume that the bases on both sides of the equation are equal. . We assume that the powers of the same base on both sides of the equation are equal.

STEP 2

First, we equate the powers of $x$ on both sides of the equation. $4 - ? =2$

STEP 3

olving the equation for the unknown, we get $? = -2$

STEP 4

Calculate the value of the unknown.
$? =4 -2 =2$ So, the power of $x$ in the denominator is2.

STEP 5

Next, we equate the powers of $y$ on both sides of the equation.
$? - (-3) = -1$

STEP 6

olving the equation for the unknown, we get $? = -1 -3$

STEP 7

Calculate the value of the unknown.
$? = -1 -3 = -4$ So, the power of $y$ in the numerator is -4.

STEP 8

Finally, we equate the powers of $z$ on both sides of the equation.
$-3 - ? =7$

STEP 9

olving the equation for the unknown, we get $? = -3 -7$

STEP 10

Calculate the value of the unknown.
$? = -3 -7 = -10$ So, the power of $z$ in the denominator is -10.
The solution is the power of $x$ in the denominator is2, the power of $y$ in the numerator is -4, and the power of $z$ in the denominator is -10.

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QuestionSolve for the unknowns in the equation: $\frac{2 x^{4} y^{?} z^{-3}}{3 x^{?} y^{-3} z^{?}}=\frac{2 x^{2}}{3 y z^{7}}$ .

Studdy Solution

STEP 1

Assumptions1. We assume that the bases on both sides of the equation are equal. . We assume that the powers of the same base on both sides of the equation are equal.

STEP 2

First, we equate the powers of $x$ on both sides of the equation. $4 - ? =2$

STEP 3

olving the equation for the unknown, we get $? = -2$

STEP 4

Calculate the value of the unknown.
$? =4 -2 =2$ So, the power of $x$ in the denominator is2.

STEP 5

Next, we equate the powers of $y$ on both sides of the equation.
$? - (-3) = -1$

STEP 6

olving the equation for the unknown, we get $? = -1 -3$

STEP 7

Calculate the value of the unknown.
$? = -1 -3 = -4$ So, the power of $y$ in the numerator is -4.

STEP 8

Finally, we equate the powers of $z$ on both sides of the equation.
$-3 - ? =7$

STEP 9

olving the equation for the unknown, we get $? = -3 -7$

STEP 10

Calculate the value of the unknown.
$? = -3 -7 = -10$ So, the power of $z$ in the denominator is -10.
The solution is the power of $x$ in the denominator is2, the power of $y$ in the numerator is -4, and the power of $z$ in the denominator is -10.

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QuestionSolve for the unknowns in the equation: 2x4y?z−33x?y−3z?=2x23yz7\frac{2 x^{4} y^{?} z^{-3}}{3 x^{?} y^{-3} z^{?}}=\frac{2 x^{2}}{3 y z^{7}}3x?y−3z?2x4y?z−3​=3yz72x2​.

Studdy Solution

STEP 1

Assumptions1. We assume that the bases on both sides of the equation are equal. . We assume that the powers of the same base on both sides of the equation are equal.

STEP 2

First, we equate the powers of xxx on both sides of the equation.4−?=24 - ? =24−?=2

STEP 3

olving the equation for the unknown, we get?=−2? = -2?=−2

STEP 4

Calculate the value of the unknown.?=4−2=2? =4 -2 =2?=4−2=2So, the power of xxx in the denominator is2.

STEP 5

Next, we equate the powers of yyy on both sides of the equation.?−(−3)=−1? - (-3) = -1?−(−3)=−1

STEP 6

olving the equation for the unknown, we get?=−1−3? = -1 -3?=−1−3

STEP 7

Calculate the value of the unknown.?=−1−3=−4? = -1 -3 = -4?=−1−3=−4So, the power of yyy in the numerator is -4.

STEP 8

Finally, we equate the powers of zzz on both sides of the equation.−3−?=7-3 - ? =7−3−?=7

STEP 9

olving the equation for the unknown, we get?=−3−7? = -3 -7?=−3−7

STEP 10

Calculate the value of the unknown.?=−3−7=−10? = -3 -7 = -10?=−3−7=−10So, the power of zzz in the denominator is -10.The solution is the power of xxx in the denominator is2, the power of yyy in the numerator is -4, and the power of zzz in the denominator is -10.

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QuestionSolve for the unknowns in the equation: $\frac{2 x^{4} y^{?} z^{-3}}{3 x^{?} y^{-3} z^{?}}=\frac{2 x^{2}}{3 y z^{7}}$ .

First, we equate the powers of $x$ on both sides of the equation. $4 - ? =2$

olving the equation for the unknown, we get $? = -2$

Calculate the value of the unknown.
$? =4 -2 =2$ So, the power of $x$ in the denominator is2.

Next, we equate the powers of $y$ on both sides of the equation.
$? - (-3) = -1$

olving the equation for the unknown, we get $? = -1 -3$

Calculate the value of the unknown.
$? = -1 -3 = -4$ So, the power of $y$ in the numerator is -4.

Finally, we equate the powers of $z$ on both sides of the equation.
$-3 - ? =7$

olving the equation for the unknown, we get $? = -3 -7$

Calculate the value of the unknown.
$? = -3 -7 = -10$ So, the power of $z$ in the denominator is -10.
The solution is the power of $x$ in the denominator is2, the power of $y$ in the numerator is -4, and the power of $z$ in the denominator is -10.