Question

Please help! (logarithmic + exponential functions)

Answer 1

1. The expression is equivalent to x⁻⁶, which corresponds to option (4).

2. The correct way to rewrite the function y = 16(2ˣ) is
`y = 2^(4+x)`. Option 3

How do we find the equivalent expressions?

1. The power rule for exponents, which states that
`(a^m)^n = a^{(m*n)`

Using this rule, The expression
`((1)/(x^3))^2` becomes
`(x^(-3))^2` =
`x^(-3*2)` = x⁻⁶

Therefore, the expression is equivalent to x⁻⁶

2. The exponential function y = 16(2ˣ) can be rewritten by incorporating the constant 16 as a power of 2 since 16 is 2⁴.

y = ( 2⁴)(2ˣ)

Using the property of exponents that
`a^m * a^n` =
`a^(m+n)`

we can combine the terms;
`y = 2^(4+x)`