Basic Math Examples

$\frac{5^{- 2} y^{- 6}}{{(2 y^{- 7})}^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Move $5^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{- 6}}{{(2 y^{- 7})}^{2} \cdot 5^{2}}$

Step 1.2

Move $y^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(2 y^{- 7})}^{2} \cdot 5^{2} y^{6}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 y^{- 7}$ .

$\frac{1}{2^{2} {(y^{- 7})}^{2} \cdot 5^{2} y^{6}}$

Step 2.2

Raise $2$ to the power of $2$ .

$\frac{1}{4 {(y^{- 7})}^{2} \cdot 5^{2} y^{6}}$

Step 2.3

Multiply the exponents in ${(y^{- 7})}^{2}$ .

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Step 2.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{4 y^{- 7 \cdot 2} \cdot 5^{2} y^{6}}$

Step 2.3.2

Multiply $- 7$ by $2$ .

$\frac{1}{4 y^{- 14} \cdot 5^{2} y^{6}}$

Step 2.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{4 \frac{1}{y^{14}} \cdot 5^{2} y^{6}}$

Step 2.5

Raise $5$ to the power of $2$ .

$\frac{1}{4 \frac{1}{y^{14}} \cdot 25 y^{6}}$

Step 2.6

Combine exponents.

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Step 2.6.1

Combine $4$ and $\frac{1}{y^{14}}$ .

$\frac{1}{\frac{4}{y^{14}} \cdot 25 y^{6}}$

Step 2.6.2

Combine $\frac{4}{y^{14}}$ and $25$ .

$\frac{1}{\frac{4 \cdot 25}{y^{14}} y^{6}}$

Step 2.6.3

Multiply $4$ by $25$ .

$\frac{1}{\frac{100}{y^{14}} y^{6}}$

Step 2.6.4

Combine $\frac{100}{y^{14}}$ and $y^{6}$ .

$\frac{1}{\frac{100 y^{6}}{y^{14}}}$

Step 2.7

Reduce the expression $\frac{100 y^{6}}{y^{14}}$ by cancelling the common factors.

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Step 2.7.1

Factor $y^{6}$ out of $100 y^{6}$ .

$\frac{1}{\frac{y^{6} \cdot 100}{y^{14}}}$

Step 2.7.2

Factor $y^{6}$ out of $y^{14}$ .

$\frac{1}{\frac{y^{6} \cdot 100}{y^{6} y^{8}}}$

Step 2.7.3

Cancel the common factor.

$\frac{1}{\frac{y^{6} \cdot 100}{y^{6} y^{8}}}$

Step 2.7.4

Rewrite the expression.

$\frac{1}{\frac{100}{y^{8}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{y^{8}}{100}$

Step 4

Multiply $\frac{y^{8}}{100}$ by $1$ .

$\frac{y^{8}}{100}$