Convert the Expression: Writing 1/5² in Standard Form

Q: Why does the exponent become negative?

The negative exponent rule shows that dividing by a power is the same as multiplying by that power with a negative sign. Think of it as flipping from division to multiplication!

Q: Does the base number change when I use negative exponents?

No! The base stays exactly the same. Only the exponent changes from positive to negative. So $ \frac{1}{5^2} $ becomes $ 5^{-2} $, not $ -5^2 $.

Q: How can I check if my negative exponent is correct?

Calculate both expressions and see if they're equal! $ \frac{1}{5^2} = \frac{1}{25} = 0.04 $ and $ 5^{-2} = 0.04 $. They match!

Q: What if the original exponent is already negative?

If you start with something like $ \frac{1}{5^{-3}} $, it becomes $ 5^3 $! The negative of a negative becomes positive.

Q: Can I use this rule with any base?

Yes! This rule works with any base: $ \frac{1}{x^n} = x^{-n} $, whether x is 2, 10, or even a variable like a or b.

Negative Exponents with Fractional Expressions

Insert the corresponding expression:

$\frac{1}{5^2}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the following problem

00:03 According to the laws of exponents, a number raised to the power of (-N)

00:06 is equal to its reciprocal raised to the opposite power (N)

00:09 We will apply this formula to our exercise

00:12 We'll convert to the reciprocal number and raise it to the opposite power (times(-1))

00:15 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the corresponding expression:

$\frac{1}{5^2}=$

Step-by-step solution

To solve the given problem, we need to express $\frac{1}{5^2}$ using negative exponents. We'll apply the formula for negative exponents, which is $\frac{1}{a^n} = a^{-n}$ :

Identify the base and power in the denominator. Here, the base is $5$ and the power is $2$ .
Apply the inverse formula: $\frac{1}{5^2} = 5^{-2}$ .

Thus, the equivalent expression for $\frac{1}{5^2}$ using a negative exponent is $5^{-2}$ .

Final Answer

$5^{-2}$

Key Points to Remember

Essential concepts to master this topic

Rule: $\frac{1}{a^n} = a^{-n}$ converts fraction to negative exponent
Technique: Base stays same, exponent becomes negative: $\frac{1}{5^2} = 5^{-2}$
Check: Verify both expressions equal same value: $\frac{1}{25} = 0.04$ ✓

Common Mistakes

Avoid these frequent errors

Making the base negative instead of the exponent
Don't change $\frac{1}{5^2}$ to $-5^2$ = -25! This creates a negative number when the original fraction is positive. Always keep the base positive and make only the exponent negative.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why does the exponent become negative?

The negative exponent rule shows that dividing by a power is the same as multiplying by that power with a negative sign. Think of it as flipping from division to multiplication!

Does the base number change when I use negative exponents?

No! The base stays exactly the same. Only the exponent changes from positive to negative. So $\frac{1}{5^2}$ becomes $5^{-2}$ , not $-5^2$ .

How can I check if my negative exponent is correct?

Calculate both expressions and see if they're equal! $\frac{1}{5^2} = \frac{1}{25} = 0.04$ and $5^{-2} = 0.04$ . They match!

What if the original exponent is already negative?

If you start with something like $\frac{1}{5^{-3}}$ , it becomes $5^3$ ! The negative of a negative becomes positive.

Can I use this rule with any base?

Yes! This rule works with any base: $\frac{1}{x^n} = x^{-n}$ , whether x is 2, 10, or even a variable like a or b.

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Convert the Expression: Writing 1/5² in Standard Form

Negative Exponents with Fractional Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does the exponent become negative?

Does the base number change when I use negative exponents?

How can I check if my negative exponent is correct?

What if the original exponent is already negative?

Can I use this rule with any base?

🌟 Unlock Your Math Potential

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