Write all 7 laws of Exponents class 7
Answers
Step-by-step explanation:
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1. Product of powers rule
When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.
42 × 45 = ?
Since the base values are both four, keep them the same and then add the exponents (2 + 5) together.
42× 45 = 47
Then multiply four by itself seven times to get the answer.
47 = 4 × 4 × 4 × 4 × 4 × 4 × 4 = 16,384
Let’s expand the above equation to see how this rule works:
e exponent rules
In an equation like this, adding the exponents together is a shortcut to get the answer.
Here’s a more complicated question to try:
(42)(23) = ?
Multiply the coefficients together (four and two), as they are not the same base. Then keep the ‘’ the same and add the exponents.
(42)(23) = 85.
2. Quotient of powers rule
Multiplication and division are opposites of each other -- much the same, the quotient rule acts as the opposite of the product rule.
When dividing two bases of the same value, keep the base the same, and then subtract the exponent values.
55 ÷ 53 = ?
Both bases in this equation are five, which means they stay the same. Then, take the exponents and subtract the divisor from the dividend.
55 ÷ 53 = 52
Finally, simplify the equation if needed:
52 = 5 × 5 = 25
Once again, expanding the equation shows us that this shortcut gives the correct answer:
basic exponent rules
Take a look at this more complicated example:
54/102 = ?
The like variables in the denominator cancel out those in the numerator. You can show your students this by crossing out an equal number of ’s from the top and bottom of the fraction.
54/102 = 5/10
Then simplify where possible, as you would with any fraction. Five can go into ten, five times turning the fraction into ½ with the remaining variables.
54/102 = 12/2 = 2/2.
3. Power of a power rule
This rule shows how to solve equations where a power is being raised by another power.
(3)3 = ?
In equations like the one above, multiply the exponents together and keep the base the same.
(3)3 = 9
Take a look at the expanded equation to see how this works:
exponent rules review worksheet.
4. Power of a product rule
When any base is being multiplied by an exponent, distribute the exponent to each part of the base.
()3 = ?
In this equation, the power of three needs to be distributed to both the and the variables.
()3 = 33
This rule applies if there are exponents attached to the base as well.
(22)3 = 66
Expanded, the equation would look like this:
exponent and log rules
Both of the variables are squared in this equation and are being raised to the power of three. That means three is multiplied to the exponents in both variables turning them into variables that are raised to the power of six.
5. Power of a quotient rule
A quotient simply means that you’re dividing two quantities. In this rule, you’re raising a quotient by a power. Like the power of a product rule, the exponent needs to be distributed to all values within the brackets it’s attached to.
(/)4 = ?
Here, raise both variables within the brackets by the power of four.
dividing exponent rules
Take a look at this more complicated equation:
(43/5 4)2 = ?
Don’t forget to distribute the exponent you’re multiplying by to both the coefficient and the variable. Then simplify where possible.
(43/54)2 = 426/528 = 166/258.
6. Zero power rule
Any base raised to the power of zero is equal to one.
math exponent rules
The easiest way to explain this rule is by using the quotient of powers rule.
43/43 = ?
Following the quotient of powers rule, subtract the exponents from each other, which cancels them out, only leaving the base. Any number divided by itself is one.
43/43 = 4/4 = 1
No matter how long the equation, anything raised to the power of zero becomes one.
(8246)0 = ?
Typically, the outside exponent would have to be multiplied throughout each number and variable in the brackets. However, since this equation is being raised to the power of zero, these steps can be skipped and the answer simply becomes one.
(8246)0 = 1
The equation fully expanded would look like this:
(8246)0 = 8000 = (1)(1)(1) = 1.
7. Negative exponent rule
When there is a number being raised by a negative exponent, flip it into a reciprocal to turn the exponent into a positive. Don’t use the negative exponent to turn the base into a negative.
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fraction exponent rules.