Solve 19^-2: Calculating a Specific Negative Exponent

Question

19−2=? 19^{-2}=\text{?}

Video Solution

Solution Steps

00:00 Solving an exercise with a negative exponent
00:03 According to the laws of exponents, any number(A)raised to the power of(N)
00:06 equals 1 divided by the number(A)raised to the power of (-N)
00:13 The number(19) becomes 1 divided by(19)
00:15 The exponent(-2) changes its sign to a positive -(2-)
00:16 and the exponent(-2) becomes -(-2)
00:19 A negative multiplied by a negative becomes a positive hence the exponent is 2
00:22 This is the solution

Step-by-Step Solution

In order to solve the exercise, we use the negative exponent rule.

a−n=1an a^{-n}=\frac{1}{a^n}

We apply the rule to the given exercise:

19−2=1192 19^{-2}=\frac{1}{19^2}

We can then continue and calculate the exponent.

1192=1361 \frac{1}{19^2}=\frac{1}{361}

Answer

1361 \frac{1}{361}

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Negative Exponents Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Exponents - Special Cases

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