13 Questions
What is another name for exponents?
Powers
What does 82 mean?
8 to the power 2
What does x0 equal to?
1
What happens to a number when the exponent is negative?
It becomes smaller
Which of the following is NOT one of the Laws of Exponents?
$x^0 = 0$
What is the key to understanding the Laws of Exponents?
Writing all the letters down
When applying the law (xm)n = xmn, how many times do we end up multiplying 'x'?
m × n times
According to the law (xy)n = xnyn, what does (xy)3 equal to?
xxxyyy
What is the result of x2/x2 according to the law xm/xn = xm-n?
x0
In the law xm/n = n√xm = (n√x )m, what does x(mn) equal to?
(xm)1/n
According to the law (x/y)n = xn/yn, what is the result of (x/y)3?
(xxx)/(yyy)
What is the value of x1/n where n is a positive integer?
The nth root of x
When simplifying x(mn) using the law x(mn) = x(m × 1/n), what is the result?
(xm)1/n
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).
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.
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