Simplify ((x^25)^-6)/((x^-3)^48)

$\frac{{(x^{25})}^{- 6}}{{(x^{- 3})}^{48}}$

Step 1

Move ${(x^{25})}^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(x^{- 3})}^{48} {(x^{25})}^{6}}$

Step 2

Simplify the denominator.

Multiply the exponents in ${(x^{- 3})}^{48}$ .

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

$\frac{1}{x^{- 3 \cdot 48} {(x^{25})}^{6}}$

Multiply $- 3$ by $48$ .

$\frac{1}{x^{- 144} {(x^{25})}^{6}}$

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

$\frac{1}{\frac{1}{x^{144}} {(x^{25})}^{6}}$

Multiply the exponents in ${(x^{25})}^{6}$ .

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

$\frac{1}{\frac{1}{x^{144}} x^{25 \cdot 6}}$

Multiply $25$ by $6$ .

$\frac{1}{\frac{1}{x^{144}} x^{150}}$

Step 3

Combine $\frac{1}{x^{144}}$ and $x^{150}$ .

$\frac{1}{\frac{x^{150}}{x^{144}}}$

Step 4

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{x^{150}}{x^{144}}$ by cancelling the common factors.

Factor $x^{144}$ out of $x^{150}$ .

$\frac{1}{\frac{x^{144} x^{6}}{x^{144}}}$

Multiply by $1$ .

$\frac{1}{\frac{x^{144} x^{6}}{x^{144} \cdot 1}}$

Cancel the common factor.

$\frac{1}{\frac{x^{144} x^{6}}{x^{144} \cdot 1}}$

Rewrite the expression.

$\frac{1}{\frac{x^{6}}{1}}$

Divide $x^{6}$ by $1$ .

$\frac{1}{x^{6}}$