Solve frac{7^{-5}}{7^-6}+[7/343-7]^0-7^3/7^2

$$\frac { 7 ^ { - 5 } } { 7 ^ { - 6 } } + [ \frac { 7 } { 343 } - 7 ] ^ { 0 } - \frac { 7 ^ { 3 } } { 7 ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from -5 to get 1.

$$7^{1}+\left(\frac{7}{343}-7\right)^{0}-\frac{7^{3}}{7^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$7^{1}+\left(\frac{7}{343}-7\right)^{0}-7^{1}$$

Calculate 7 to the power of 1 and get 7.

$$7+\left(\frac{7}{343}-7\right)^{0}-7^{1}$$

Reduce the fraction \frac{7}{343} to lowest terms by extracting and canceling out 7.

$$7+\left(\frac{1}{49}-7\right)^{0}-7^{1}$$

Subtract 7 from \frac{1}{49} to get -\frac{342}{49}.

$$7+\left(-\frac{342}{49}\right)^{0}-7^{1}$$

Calculate -\frac{342}{49} to the power of 0 and get 1.

$$7+1-7^{1}$$

Add 7 and 1 to get 8.

$$8-7^{1}$$

Calculate 7 to the power of 1 and get 7.

$$8-7$$

Subtract 7 from 8 to get 1.

$$1$$

Factor

$$1$$