Math / Algebra

QuestionSimplify. Rewrite the expression in the form $y^{n}$ . $\frac{y^{-7}}{y^{-13}}=$ $\square$

Studdy Solution

STEP 1

1. We are asked to simplify the expression and rewrite it in the form $y^n$ .
2. The laws of exponents can be applied to simplify the expression.

STEP 2

1. Apply the quotient rule for exponents.
2. Simplify the resulting expression.

STEP 3

Apply the quotient rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{y^{-7}}{y^{-13}} = y^{-7 - (-13)}$

STEP 4

Simplify the exponent by performing the subtraction:
$-7 - (-13) = -7 + 13 = 6$

STEP 5

Rewrite the expression using the simplified exponent:
$y^6$
The simplified expression is:
$\boxed{y^6}$

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QuestionSimplify. Rewrite the expression in the form $y^{n}$ . $\frac{y^{-7}}{y^{-13}}=$ $\square$

Studdy Solution

STEP 1

1. We are asked to simplify the expression and rewrite it in the form $y^n$ .
2. The laws of exponents can be applied to simplify the expression.

STEP 2

1. Apply the quotient rule for exponents.
2. Simplify the resulting expression.

STEP 3

Apply the quotient rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{y^{-7}}{y^{-13}} = y^{-7 - (-13)}$

STEP 4

Simplify the exponent by performing the subtraction:
$-7 - (-13) = -7 + 13 = 6$

STEP 5

Rewrite the expression using the simplified exponent:
$y^6$
The simplified expression is:
$\boxed{y^6}$

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QuestionSimplify. Rewrite the expression in the form yny^{n}yn. y−7y−13=\frac{y^{-7}}{y^{-13}}=y−13y−7​= □\square□

Studdy Solution

STEP 1

1. We are asked to simplify the expression and rewrite it in the form yn y^n yn.2. The laws of exponents can be applied to simplify the expression.

STEP 2

1. Apply the quotient rule for exponents.2. Simplify the resulting expression.

STEP 3

Apply the quotient rule for exponents, which states that aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n.y−7y−13=y−7−(−13) \frac{y^{-7}}{y^{-13}} = y^{-7 - (-13)} y−13y−7​=y−7−(−13)

STEP 4

Simplify the exponent by performing the subtraction:−7−(−13)=−7+13=6 -7 - (-13) = -7 + 13 = 6 −7−(−13)=−7+13=6

STEP 5

Rewrite the expression using the simplified exponent:y6 y^6 y6 The simplified expression is:y6 \boxed{y^6} y6​

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Start learning now

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QuestionSimplify. Rewrite the expression in the form $y^{n}$ . $\frac{y^{-7}}{y^{-13}}=$ $\square$

1. We are asked to simplify the expression and rewrite it in the form $y^n$ .
2. The laws of exponents can be applied to simplify the expression.

1. Apply the quotient rule for exponents.
2. Simplify the resulting expression.

Apply the quotient rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{y^{-7}}{y^{-13}} = y^{-7 - (-13)}$

Simplify the exponent by performing the subtraction:
$-7 - (-13) = -7 + 13 = 6$

Rewrite the expression using the simplified exponent:
$y^6$
The simplified expression is:
$\boxed{y^6}$