Which of the following is an equivalent expression to 15⁰×7-²/(-4)-³ with only positive exponents that had been generated by applying the properties of integer exponents?
The expression 15⁰×7-²/(-4)-³, using the properties of integer exponents, can be simplified as follows:
First, any number raised to the power of 0 is equal to 1, so 15⁰ = 1.
Next, a negative exponent can be rewritten as the reciprocal with a positive exponent. 7-² = 1/7² = 1/49.
Similarly, (-4)-³ = 1/(-4)³ = 1/(-64) = -1/64.
Now we can substitute these simplified values back into the original expression: 1 × 1/49 / (-1/64)
Dividing by a fraction is equivalent to multiplying by its reciprocal, so we can rewrite it as: 1 × 1/49 × (-64/1)
Multiplying these fractions together, we get: (1 × 1 × -64) / (49 × 1)
Simplifying further, we have: -64/49
Therefore, an equivalent expression to 15⁰×7-²/(-4)-³ with only positive exponents is -64/49.
To simplify the given expression and rewrite it with only positive exponents, we can use the properties of integer exponents. Let's break down each part of the expression:
1. 15⁰: Any number raised to the power of 0 is equal to 1. So, 15⁰ = 1.
2. 7-²: To get rid of the negative exponent, we can use the property that says if a number is raised to a negative exponent, we can rewrite it as 1 divided by the number raised to the positive exponent. Therefore, 7-² can be rewritten as 1/7² = 1/49.
3. (-4)-³: Similar to the previous example, we can rewrite this as 1/(-4)³ = 1/(-64) since a negative number raised to an odd exponent remains negative.
Now, let's put all the simplified parts together:
1 × 1/49 ÷ 1/(-64)
When dividing by a fraction, we can multiply by its reciprocal instead. So, the expression becomes:
1 × 1/49 × (-64)/1
Multiplying the numerators together and the denominators together, we get:
-64/49
Therefore, an equivalent expression to 15⁰ × 7-² / (-4)-³ with only positive exponents is -64/49.
To simplify the given expression and convert the exponents to positive values, we can apply the properties of integer exponents.
First, let's simplify the expression 7-². The property of integer exponents states that a number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent. Therefore, 7-² = 1 / 7² = 1/49.
Next, let's simplify the expression -4-³. Similarly, using the property of integer exponents, -4-³ = 1 / (-4)³ = 1 / (-64) = -1/64.
Now, let's substitute the simplified values back into the original expression: 15⁰ × 1/49 × -1/64.
To simplify further, we need to simplify 15⁰. Any number (except 0) raised to the power of 0 is always equal to 1. Therefore, 15⁰ = 1.
Now, we substitute the simplified values back into the expression: 1 × 1/49 × -1/64.
To multiply fractions, we multiply the numerators together and multiply the denominators together. So, 1/49 × -1/64 = (-1/49)(1/64) = -1/(49*64) = -1/3136.
Therefore, the expression 15⁰ × 7-² / (-4) -³, with only positive exponents and generated by applying the properties of integer exponents, simplified to -1/3136.