Solve [(0/8)^{1}]^2:(9/8)^4=(9/8)^16(9/8)^2

$$[ ( \frac { 0 } { 8 } ) ^ { 1 } ] ^ { 2 } : ( \frac { 9 } { 8 } ) ^ { 4 } = ( \frac { 9 } { 8 } ) ^ { 16 } ( \frac { 9 } { 8 } ) ^ { 2 }$$

Verify

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 1 and 2 to get 2.

$$\frac{\left(\frac{0}{8}\right)^{2}}{\left(\frac{9}{8}\right)^{4}}=\left(\frac{9}{8}\right)^{16}\times \left(\frac{9}{8}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 16 and 2 to get 18.

$$\frac{\left(\frac{0}{8}\right)^{2}}{\left(\frac{9}{8}\right)^{4}}=\left(\frac{9}{8}\right)^{18}$$

Zero divided by any non-zero number gives zero.

$$\frac{0^{2}}{\left(\frac{9}{8}\right)^{4}}=\left(\frac{9}{8}\right)^{18}$$

Calculate 0 to the power of 2 and get 0.

$$\frac{0}{\left(\frac{9}{8}\right)^{4}}=\left(\frac{9}{8}\right)^{18}$$

Calculate \frac{9}{8} to the power of 4 and get \frac{6561}{4096}.

$$\frac{0}{\frac{6561}{4096}}=\left(\frac{9}{8}\right)^{18}$$

Zero divided by any non-zero number gives zero.

$$0=\left(\frac{9}{8}\right)^{18}$$

Calculate \frac{9}{8} to the power of 18 and get \frac{150094635296999121}{18014398509481984}.

$$0=\frac{150094635296999121}{18014398509481984}$$

Compare 0 and \frac{150094635296999121}{18014398509481984}.

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