Solve [(-4)^{11}*(-4)^{8}]=(-4)^17+(-4)^13:[(-4)^6]^2

$$[ ( - 4 ) ^ { 11 } \cdot ( - 4 ) ^ { 8 } ] = ( - 4 ) ^ { 17 } + ( - 4 ) ^ { 13 } : [ ( - 4 ) ^ { 6 } ] ^ { 2 }$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 11 and 8 to get 19.

$$\left(-4\right)^{19}=\left(-4\right)^{17}+\frac{\left(-4\right)^{13}}{\left(\left(-4\right)^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(-4\right)^{19}=\left(-4\right)^{17}+\frac{\left(-4\right)^{13}}{\left(-4\right)^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 13 to get 1.

$$\left(-4\right)^{19}=\left(-4\right)^{17}+\left(-4\right)^{1}$$

Calculate -4 to the power of 19 and get -274877906944.

$$-274877906944=\left(-4\right)^{17}+\left(-4\right)^{1}$$

Calculate -4 to the power of 17 and get -17179869184.

$$-274877906944=-17179869184+\left(-4\right)^{1}$$

Calculate -4 to the power of 1 and get -4.

$$-274877906944=-17179869184-4$$

Subtract 4 from -17179869184 to get -17179869188.

$$-274877906944=-17179869188$$

Compare -274877906944 and -17179869188.

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