Simplify and write the answer in the exponential form.
$(9^{16} \div 9^{14}) \times 9$

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Solution

Hint: We know the law of exponents that is powers with same base: $x^{a} \div x^{b} = x^{a - b}$ And $x^{a} \times x^{b} = x^{a + b}$
Step :Compute the required value.
Given expression: $(9^{16} \div 9^{14}) \times 9$
Using the above law:
$(9^{16} \div 9^{14}) \times 9 = (9^{16 - 14}) \times 9 \{x^{a} \div x^{b} = x^{a - b}\} = (9^{2}) \times 9 = 9^{2 + 1} \{x^{a} \times x^{b} = x^{a + b}\} = 9^{3}$
Hence, $9^{3}$ , is the required exponential form.

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