Simplify (120^(-2/5)*120^(2/5))/(7^(-3/4))

$\frac{120^{- \frac{2}{5}} \cdot 120^{\frac{2}{5}}}{7^{- \frac{3}{4}}}$

Multiply $120^{- \frac{2}{5}}$ by $120^{\frac{2}{5}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{120^{- \frac{2}{5} + \frac{2}{5}}}{7^{- \frac{3}{4}}}$

Combine the numerators over the common denominator.

$\frac{120^{\frac{- 2 + 2}{5}}}{7^{- \frac{3}{4}}}$

Add $- 2$ and $2$ .

$\frac{120^{\frac{0}{5}}}{7^{- \frac{3}{4}}}$

Divide $0$ by $5$ .

$\frac{120^{0}}{7^{- \frac{3}{4}}}$

Simplify $120^{0}$ .

$\frac{1}{7^{- \frac{3}{4}}}$

Move $7^{- \frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$7^{\frac{3}{4}}$

The result can be shown in multiple forms.

Exact Form:

$7^{\frac{3}{4}}$

Decimal Form:

$4.30351707 \dots$