Expand the Expression: Converting 10^-1 to Decimal Form

Expand the following expression:

10−1= 10^{-1}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Identify which expressions are equal to the original expression
00:03 According to the laws of exponents, the multiplication of powers with equal bases (A)
00:06 equals the same base raised to the sum of the exponents (N+M)
00:09 Let's apply this formula to our exercise
00:12 We'll maintain the base and add up the exponents
00:15 This expression is equal to the original expression
00:18 Let's use the same method in order to simplify the remaining expressions
00:21 This expression is not equal to the original expression
00:34 This expression is not equal to the original expression
00:39 This expression is also not equal to the original expression
00:45 This is the solution

Step-by-step written solution

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1

Understand the problem

Expand the following expression:

10−1= 10^{-1}=

2

Step-by-step solution

Let's solve the problem step by step:

The expression given is 10−1 10^{-1} . A negative exponent indicates a reciprocal, so:

10−1=110 10^{-1} = \frac{1}{10}

We can express this as a multiplication form of powers of 10:

Using the property of exponents, specifically the multiplication of powers, we can rewrite:

110=10−11×1010 \frac{1}{10} = 10^{-11} \times 10^{10}

To verify:

  • Apply the rule of exponents: 10−11×1010=10−11+10=10−1 10^{-11} \times 10^{10} = 10^{-11 + 10} = 10^{-1}

  • This confirms the expression is correctly transformed back to 10−1 10^{-1} .

Thus, the expanded expression of 10−1 10^{-1} is:

10−11×1010 10^{-11}\times10^{10}

3

Final Answer

10−11×1010 10^{-11}\times10^{10}

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\( (4^3)^2= \)

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