Podcast
Questions and Answers
What is another name for exponents?
What is another name for exponents?
What does 82 mean?
What does 82 mean?
What does x0 equal to?
What does x0 equal to?
What happens to a number when the exponent is negative?
What happens to a number when the exponent is negative?
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Which of the following is NOT one of the Laws of Exponents?
Which of the following is NOT one of the Laws of Exponents?
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What is the key to understanding the Laws of Exponents?
What is the key to understanding the Laws of Exponents?
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When applying the law (xm)n = xmn, how many times do we end up multiplying 'x'?
When applying the law (xm)n = xmn, how many times do we end up multiplying 'x'?
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According to the law (xy)n = xnyn, what does (xy)3 equal to?
According to the law (xy)n = xnyn, what does (xy)3 equal to?
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What is the result of x2/x2 according to the law xm/xn = xm-n?
What is the result of x2/x2 according to the law xm/xn = xm-n?
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In the law xm/n = n√xm = (n√x )m, what does x(mn) equal to?
In the law xm/n = n√xm = (n√x )m, what does x(mn) equal to?
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According to the law (x/y)n = xn/yn, what is the result of (x/y)3?
According to the law (x/y)n = xn/yn, what is the result of (x/y)3?
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What is the value of x1/n where n is a positive integer?
What is the value of x1/n where n is a positive integer?
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When simplifying x(mn) using the law x(mn) = x(m × 1/n), what is the result?
When simplifying x(mn) using the law x(mn) = x(m × 1/n), what is the result?
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Study Notes
Exponents
- Exponents are also known as indices or powers.
Exponent Notation
- The notation 82 means 8 raised to the power of 2, or 8 squared.
- Any number raised to the power of 0 equals 1.
Negative Exponents
- When a number has a negative exponent, it becomes a reciprocal (i.e., 1 divided by the number).
Laws of Exponents
- The key to understanding the Laws of Exponents is to recognize that exponents are a shorthand for repeated multiplication.
- One of the Laws of Exponents is not "x^m × x^n = x^(m+n+c)", where c is a constant.
Power of a Power
- When applying the law (xm)n = xmn, we end up multiplying 'x' mn times.
Product of Powers
- According to the law (xy)n = xnyn, (xy)3 equals to x3y3.
Quotient of Powers
- The result of x2/x2 according to the law xm/xn = xm-n is 1 (since 2-2 = 0).
Power of a Product
- In the law xm/n = n√xm = (n√x)m, x(mn) equals to (n√x)m.
- According to the law (x/y)n = xn/yn, the result of (x/y)3 is x3/y3.
Fractional Exponents
- The value of x1/n, where n is a positive integer, is the nth root of x.
Simplifying Exponents
- When simplifying x(mn) using the law x(mn) = x(m × 1/n), the result is x(m/n).
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Description
Test your knowledge about the laws of exponents, also known as powers or indices. Learn how exponents indicate the number of times to use a number in multiplication, and practice simplifying expressions using exponent rules.
