Solve d. [(- a ^ - 5)/(- a ^ 10 * b ^ - 9 * c ^ - 7 * (a ^ - 15 * c ^ 0))] ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

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Question

$$[ \frac { - a ^ { - 5 } } { - a ^ { 10 } b ^ { - 9 } c ^ { - 7 } \times ( a ^ { - 15 } \times c ^ { 0 } ) } ] ^ { 2 }$$

Evaluate

$c^{14}b^{18}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $-7$ and $0$ to get $-7$.

$$\left(\frac{-a^{-5}}{\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}}\right)^{2}$$

To raise $\frac{-a^{-5}}{\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-a^{-5}\right)^{2}}{\left(\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}\right)^{2}}$$

Calculate $-a^{-5}$ to the power of $2$ and get $\left(a^{-5}\right)^{2}$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}\right)^{2}}$$

Expand $\left(\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}\right)^{2}$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(-a^{10}\right)^{2}\left(b^{-9}\right)^{2}\left(c^{-7}\right)^{2}\left(a^{-15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $-9$ and $2$ to get $-18$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(-a^{10}\right)^{2}b^{-18}\left(c^{-7}\right)^{2}\left(a^{-15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $-7$ and $2$ to get $-14$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(-a^{10}\right)^{2}b^{-18}c^{-14}\left(a^{-15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $-15$ and $2$ to get $-30$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(-a^{10}\right)^{2}b^{-18}c^{-14}a^{-30}}$$

Calculate $-a^{10}$ to the power of $2$ and get $\left(a^{10}\right)^{2}$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(a^{10}\right)^{2}b^{-18}c^{-14}a^{-30}}$$

To raise a power to another power, multiply the exponents. Multiply $10$ and $2$ to get $20$.

$$\frac{\left(a^{-5}\right)^{2}}{a^{20}b^{-18}c^{-14}a^{-30}}$$

To multiply powers of the same base, add their exponents. Add $20$ and $-30$ to get $-10$.

$$\frac{\left(a^{-5}\right)^{2}}{a^{-10}b^{-18}c^{-14}}$$

To raise a power to another power, multiply the exponents. Multiply $-5$ and $2$ to get $-10$.

$$\frac{a^{-10}}{a^{-10}b^{-18}c^{-14}}$$

Cancel out $a^{-10}$ in both numerator and denominator.

$$\frac{1}{b^{-18}c^{-14}}$$

Expand

$c^{14}b^{18}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $-7$ and $0$ to get $-7$.

$$\left(\frac{-a^{-5}}{\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}}\right)^{2}$$

To raise $\frac{-a^{-5}}{\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-a^{-5}\right)^{2}}{\left(\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}\right)^{2}}$$

Calculate $-a^{-5}$ to the power of $2$ and get $\left(a^{-5}\right)^{2}$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}\right)^{2}}$$

Expand $\left(\left(-a^{10}\right)b^{-9}c^{-7}a^{-15}\right)^{2}$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(-a^{10}\right)^{2}\left(b^{-9}\right)^{2}\left(c^{-7}\right)^{2}\left(a^{-15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $-9$ and $2$ to get $-18$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(-a^{10}\right)^{2}b^{-18}\left(c^{-7}\right)^{2}\left(a^{-15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $-7$ and $2$ to get $-14$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(-a^{10}\right)^{2}b^{-18}c^{-14}\left(a^{-15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $-15$ and $2$ to get $-30$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(-a^{10}\right)^{2}b^{-18}c^{-14}a^{-30}}$$

Calculate $-a^{10}$ to the power of $2$ and get $\left(a^{10}\right)^{2}$.

$$\frac{\left(a^{-5}\right)^{2}}{\left(a^{10}\right)^{2}b^{-18}c^{-14}a^{-30}}$$

To raise a power to another power, multiply the exponents. Multiply $10$ and $2$ to get $20$.

$$\frac{\left(a^{-5}\right)^{2}}{a^{20}b^{-18}c^{-14}a^{-30}}$$

To multiply powers of the same base, add their exponents. Add $20$ and $-30$ to get $-10$.

$$\frac{\left(a^{-5}\right)^{2}}{a^{-10}b^{-18}c^{-14}}$$

To raise a power to another power, multiply the exponents. Multiply $-5$ and $2$ to get $-10$.

$$\frac{a^{-10}}{a^{-10}b^{-18}c^{-14}}$$

Cancel out $a^{-10}$ in both numerator and denominator.

$$\frac{1}{b^{-18}c^{-14}}$$