how do you solve these problems
(5x)to the power of a+4(5x)to the power of a-2
3 to the power of 5 times xto the power of y+4 divided by 9 times x to the power of y
factor 5aa-2 , which is the greatest common factor, out.
5aa-2(25x2 + 4)
check my thinking.
In the second, muliply the numerator and denominator by x to the power of -y.
To solve the first problem, we have:
(5x)^(a+4) * (5x)^(a-2)
To simplify this expression, we can use the rule that says "when you raise an exponent to another exponent, you multiply the exponents." Applying this rule, we get:
(5x)^(2a+2)
For the second problem, we have:
(3^5 * x^(y+4)) / (9 * x^y)
To simplify this expression, we can first simplify the numerator and denominator separately, and then divide them.
Nominator:
3^5 = 3 * 3 * 3 * 3 * 3 = 243
x^(y+4)
Denominator:
9 = 3 * 3
x^y
Now we can divide the numerator by the denominator:
(243 * x^(y+4)) / (3 * x^y)
Lastly, to factor 5a^(a-2), we need to identify the greatest common factor. In this case, it is 5a^(a-2). Therefore, the factoring becomes:
5a^(a-2) * (25x^2 + 4)
To verify your thinking, you correctly factored the expression as 5a^(a-2)(25x^2 + 4).
In the second problem, to multiply the numerator and denominator by x^(-y), we have:
[(3^5 * x^(y+4)) * x^(-y)] / [9 * x^y * x^(-y)]
By applying the rule of multiplying exponents, we can simplify this expression:
(243 * x^(y+4-y)) / 9
Simplifying further, we get:
(243 * x^4) / 9