Simplify the expression.
1.((3)/(2b^4))^3
((27)/(8b^12))
2.((t^4)/(10y^4))^-4
(10000y^16)/(t^16)
3. Does the rule y = -3(4^x) represent an exponential function?
Yes?
1.((3)/(2b^4))^3
((27)/(8b^12)) Yes
2.((t^4)/(10y^4))^-4
(10000y^16)/(t^16) Yes
3. Does the rule y = -3(4^x) represent an exponential function?
an exponential function is a constant raised to the power of the argument.
So Yes
To simplify an expression like ((3)/(2b^4))^3, you need to raise the entire fraction to the power of 3. This means you raise the numerator and denominator to the power of 3 separately.
The numerator becomes (3^3) = 27.
The denominator becomes (2b^4)^3 = (2^3)(b^12) = 8b^12.
So the simplified expression is (27)/(8b^12).
For ((t^4)/(10y^4))^-4, you need to raise the entire fraction to the power of -4. This means you raise the numerator and denominator to the power of -4 separately.
The numerator becomes (t^4)^-4 = t^(-16) = 1/(t^16).
The denominator becomes (10y^4)^-4 = (10^-4)(y^4*-4) = 1/(10^-4)(y^16) = 10,000y^16.
So the simplified expression is (10,000y^16)/(t^16).
Regarding the function y = -3(4^x), yes, it represents an exponential function because it is in the form y = ab^x, where a = -3 and b = 4. In an exponential function, the independent variable (x) is in the exponent, and the base (b) is a constant greater than 0.