Solve frac{(a^{3}*a^-4)^3}{a^5:a^7}

$$\frac { ( a ^ { 3 } \cdot a ^ { - 4 } ) ^ { 3 } } { a ^ { 5 } : a ^ { 7 } }$$

Evaluate

$$\frac{1}{a}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$\frac{\left(a^{-1}\right)^{3}}{\frac{a^{5}}{a^{7}}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\frac{a^{-3}}{\frac{a^{5}}{a^{7}}}$$

Rewrite a^{7} as a^{5}a^{2}. Cancel out a^{5} in both numerator and denominator.

$$\frac{a^{-3}}{\frac{1}{a^{2}}}$$

Divide a^{-3} by \frac{1}{a^{2}} by multiplying a^{-3} by the reciprocal of \frac{1}{a^{2}}.

$$a^{-3}a^{2}$$

To multiply powers of the same base, add their exponents. Add -3 and 2 to get -1.

$$a^{-1}$$

Expand

$$\frac{1}{a}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$\frac{\left(a^{-1}\right)^{3}}{\frac{a^{5}}{a^{7}}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\frac{a^{-3}}{\frac{a^{5}}{a^{7}}}$$

Rewrite a^{7} as a^{5}a^{2}. Cancel out a^{5} in both numerator and denominator.

$$\frac{a^{-3}}{\frac{1}{a^{2}}}$$

Divide a^{-3} by \frac{1}{a^{2}} by multiplying a^{-3} by the reciprocal of \frac{1}{a^{2}}.

$$a^{-3}a^{2}$$

To multiply powers of the same base, add their exponents. Add -3 and 2 to get -1.

$$a^{-1}$$