Power to a Power — Rules & Examples
Read this topicExplanations 3
- (Videos) Power of a Power and Power of a Product by ThinkwellVids Here's some more videos by ThinkwellVids showing you how to take a power of a power and how you take a product …
By Alex Federspiel, Zora Gilbert, Amy Feraco, Joshua Siktar
- Power Rule for Exponents How do you raise a power to a power? In this formula, aaa, bbb, and xxx are all real numbers. We plug in values for each number and simplify. This is an…
By Caroline K, Alex Federspiel, Joshua Siktar
- (Video) Basic Exponent Properties by PatrickJMT Patrick JMT has a good video explaining the basic properties of exponents. Summary\large{\text{Summary}}Summary Recall that an ex…
By Ben Ferrara, Alex Federspiel, Joshua Siktar
Problems 40
- What is (y2)6(y^2)^6(y2)6?
- If w≠0w\ne0w=0, what is (w−3)2(w^{-3})^2(w−3)2?
- What is (3−1)−3(3^{-1})^{-3}(3−1)−3?
- What is 5(k−8)−45(k^{-8})^{-4}5(k−8)−4, if k≠0k\ne0k=0?
- What is 4(q5)−24(q^{5})^{-2}4(q5)−2 if q≠0q\ne0q=0?
- Simplify (4x2)6(4x^2)^6(4x2)6
- (23)4=(2^3)^4=(23)4=
- Simplify (3x2y)5(3x^2y)^5(3x2y)5
- Simplify (3x2×4x5)3(3x^2\times4x^5)^3(3x2×4x5)3
- Simplify (12x4y636x6)3\left(\frac{12x^4y^6}{36x^6}\right)^3(36x612x4y6)3
- Simplify (3x5y−3 )2(3y42x2 )−3\bigg(\frac{3x}{5y^{-3}}\ \bigg)^{2}\bigg(\frac{3y^4}{2x^2}\ \bigg)^{-3}(5y−33x )2(2x23y4 )−3
- Simplify ((3x−2y7)4(y−4z7)−1(x3y−2)−3(−2x−2y6z−2)3 )2\Bigg(\frac{(3x^{-2}y^7)^4(y^{-4}z^7)^{-1}}{(x^3y^{-2})^{-3}(-2x^{-2}y^6z^{-2})^3}\ \Bigg)^2((x3y−2)−3(−2x−2y6z−2)3(3x−2y7)4…
- Simplify the following expression: x3×(x2)4x^3\times (x^2)^4x3×(x2)4
- Simplify the following expression: y2×(y4)2y^2\times (y^4)^2y2×(y4)2
- Simplify the following expression: x3×(y5)3x^3\times (y^5)^3x3×(y5)3
- Simplify the following expression: a2×(a4)3×(a2)2a^2\times (a^4)^3\times (a^2)^2a2×(a4)3×(a2)2
- Simplify the following expression: a3×(a2)−1×(a3)2a^3\times (a^2)^{-1}\times (a^3)^2a3×(a2)−1×(a3)2
- Select the expression that is equivalent to (x2)3.(x^2)^3.(x2)3.
- Select the expression that is equivalent to (x−2)3×(y3)−2(x^{-2})^3\times (y^3)^{-2}(x−2)3×(y3)−2
- Find the integer value of nnn that satisfies (x2)n=x6(x^2)^n=x^6(x2)n=x6 for x>0x>0x>0.
- Find the integer value of nnn that satisfies (x2)n×x=x11(x^2)^n\times x=x^{11}(x2)n×x=x11 for x>0x>0x>0.
- Find the integer value of nnn that satisfies (yn)4×y2=y10(y^n)^4\times y^2=y^{10}(yn)4×y2=y10 for all y>0y >0y>0.
- If (xn)2=(x4)4(x^n)^2=(x^4)^4(xn)2=(x4)4 for x>0x >0x>0, what is the integer value of nnn?
- Which of the following is another way to write this expression?(x2)×(x2)×(x2)(y5)×(y5)\frac{(x^2)\times (x^2)\times (x^2)}{(y^5)\times (y^5)}(y5)×(y5)(x2)×(x2)×(x2) (Select all…
- What is (x2)5(x^{2})^5(x2)5?
- What is (y3)3(y^{3})^3(y3)3?
- What is (2x2)3(2x^2)^{3}(2x2)3?
- What is (z4)5(z^4)^5(z4)5?
- What is (23)2(2^{3})^2(23)2?
- What is (42)2(4^{2})^{2}(42)2?
- What is (32)2(3^2)^2(32)2?
- What is (43)−1(4^3)^{-1}(43)−1?
- 25×832^5\times 8^325×83 Evaluate the expression above. Hint: use both the power rule and the product rule.
- 163+64216^3+64^2163+642 Evaluate the expression.
- (−27)4×93(-27)^4\times \sqrt[3]{9}(−27)4×39 Evaluate.
- (213523)9\left(2^{\frac{1}{3}}5^{\frac{2}{3}}\right)^{^9}(231532)9 Evaluate.
- 13×(35)7\frac{1}{3}\times\left(3^5\right)^731×(35)7 Evaluate.
- Simplify the following: ((x−3)−2)−4((x^{-3})^{-2})^{-4}((x−3)−2)−4
- Simplify the following: (x2)6⋅(x3)4(x^2)^6\cdot(x^3)^4(x2)6⋅(x3)4
- After simplification, what is the exponent of xxx? (x32)3(x^{3^2})^3(x32)3