Solve (b^7/4^5)^-3

$$( \frac { b ^ { 7 } } { 4 ^ { 5 } } ) ^ { - 3 }$$

Evaluate

$$\frac{1073741824}{b^{21}}$$

Solution Steps

Calculate 4 to the power of 5 and get 1024.

$$\left(\frac{b^{7}}{1024}\right)^{-3}$$

To raise \frac{b^{7}}{1024} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{7}\right)^{-3}}{1024^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -3 to get -21.

$$\frac{b^{-21}}{1024^{-3}}$$

Calculate 1024 to the power of -3 and get \frac{1}{1073741824}.

$$\frac{b^{-21}}{\frac{1}{1073741824}}$$

Divide b^{-21} by \frac{1}{1073741824} by multiplying b^{-21} by the reciprocal of \frac{1}{1073741824}.

$$b^{-21}\times 1073741824$$

Expand

$$\frac{1073741824}{b^{21}}$$

Solution Steps

Calculate 4 to the power of 5 and get 1024.

$$\left(\frac{b^{7}}{1024}\right)^{-3}$$

To raise \frac{b^{7}}{1024} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{7}\right)^{-3}}{1024^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -3 to get -21.

$$\frac{b^{-21}}{1024^{-3}}$$

Calculate 1024 to the power of -3 and get \frac{1}{1073741824}.

$$\frac{b^{-21}}{\frac{1}{1073741824}}$$

Divide b^{-21} by \frac{1}{1073741824} by multiplying b^{-21} by the reciprocal of \frac{1}{1073741824}.

$$b^{-21}\times 1073741824$$