Multiply & Divide
Simplify y^7 / y^2
y^5. When dividing powers with the same base, subtract the exponents: 7 - 2 = 5.
simplify (3a)^2 and explain why.
9a^2. Square both factors 3^2 = 9 and a^2 stays a^2
y0 . x0 Simplify and explain
1, Anything raised to 0 is valued at 1.
Simplify the square root of 20 and explain why.
2√5. Since 20 = 4 * 5 and the square root of 4 is 2, take 2 outside the radical.
Simplify (a^5 * a^2) / a^3 and explain why.
a^4. Add the exponents when multiplying, then subtract when dividing: 5 + 2 - 3 = 4.
simplify (m/n)^3 and explain why.
M^3/N^3. The exponent applies to both the numerator and denominator because the entire fraction is raised to the third power.
2-4 Simplify and Explain.
1/24 To make the negative positive, the place needs to change.
Simplify the square root of 48 and explain why.
4√3. Since 48 = 16 * 3 and the square root of 16 is 4, the simplified form is 4√3.
Why do we add exponents when multiplying powers with the same base?
Because the factors combine into one power with the same base. For example, x^3 * x^4 has seven total factors of x, so it equals x^7.
simplify (2x^2)^3 and explain why.
8x^6. raise 2 to the third power to get 8, and multiply the exponents on 2 * 3 = 6
x0 * y-2 simplify and explain why?
1/y2 anything raised to 0 is 1. Then the y changes places.
Simplify the square root of 75 and explain why.
5√3. Since 75 = 25 * 3 and the square root of 25 is 5, the simplified form is 5√3.
Simplify (x^6 * x^3) / x^2 and explain why.
x^7. First add 6 + 3 = 9, then subtract 2: 9 - 2 = 7.
Simplify (2u3)2 and explain why.
4u6 The 2 gets raised to the 2 which is 4. 3 times 2 is six.
2x0/4y0 simplify and explain why?
1/2 The variables equal one due to the 0 exponent. Then divide bases.
Simplify the square root of 80 and explain why.
4√5. Since 80 = 16 * 5 and the square root of 16 is 4, the simplified form is 4√5.
Simplify x3 * x4
x3 * x4 = x7
(xy)4 . (y3)2 Simplify and explain.
x4y10 Raise the x and y by 4. Then multiply 3 by 2. Then add the exponents of y
Simplify 3^(-2) * 3^4 and explain why.
Add the exponents because the bases are the same: -2 + 4 = 2, so the expression equals 3^2 = 9.
Simplify the square root of 108 and explain why.
6√3. Since 108 = 36 * 3 and the square root of 36 is 6, the simplified form is 6√3.
A student says (x^2)^3 = x^5. Explain why the student is wrong and give the correct answer.
The student added the exponents instead of multiplying them. When a power is raised to another power, multiply the exponents: 2 * 3 = 6. The correct answer is x^6.