Question

What is the missing exponent?w^3 x w^? = w^-6

Answer 1

Let the missing exponent be a,

`w^3* w^a=w^(-6)`

From the law of indices stated below which satisfies the above equation,

`\begin{gathered} x^a* x^b=x^(a+b) \\ \text{relating the equation to the formula,} \\ w^3* w^a=w^(-6) \\ w^(3+a)_{}=w^(-6) \\ \text{solving the exponents,} \\ 3+a=-6 \\ \text{Collect like terms} \\ a=-6-3 \\ a=-9 \end{gathered}`

Hence, the missing exponent a is -9.