Simplify using the exponent laws #2

Hi guys,

the task: Simplify using the exponent laws. Write the final answer using only positive exponents. Evaluate where possible.

1. 2x^-1

my answer:

2

---

x

Is that right?

2. (5p^3)^-2

my answer:

1

-----

(5p^3)^2

= 1

-------

10p^6

Is that right?

3. (-32x^-10 y^15)^1/5

my answer:

(-32)^1/5 (x^-10)^1/5 (y^15)^1/5

How can I simplify further???

4. ( x^1/2 ) ^1/2

(------------)

(x^1/3 x^1/5)

the whole task is in one bracket and ^1/2 is outside the bracket.

How can I simplify?

Re: Simplify using the exponent laws #2

Quote:

Originally Posted by

**ford2008** Hi guys,

the task: Simplify using the exponent laws. Write the final answer using only positive exponents. Evaluate where possible.

1. 2x^-1

my answer:

2

---

x

Is that right? **<--- yes**

2. (5p^3)^-2

my answer:

1

-----

(5p^3)^2

= 1

-------

10p^6

Is that right? **<--- no, because 5^2 = 25**

3. (-32x^-10 y^15)^1/5

my answer:

(-32)^1/5 (x^-10)^1/5 (y^15)^1/5

How can I simplify further??? **<--- The exponents must be multiplied. ... and 32 = 2^5**

4. ( x^1/2 ) ^1/2

(------------)

(x^1/3 x^1/5)

the whole task is in one bracket and ^1/2 is outside the bracket.

How can I simplify? **<--- Simplify first the term in the large bracket:**

$\displaystyle \left(\frac{x^\frac12}{x^\frac13 \cdot x^\frac15}\right)^\frac12=\left(\frac{x^\frac12}{x ^\frac8{15}}\right)^\frac12 = \left({x^{-\frac1{30}}\right)^\frac12$

See my remark at #3.

Re: Simplify using the exponent laws #2

could you please explain more no. 3?

Re: Simplify using the exponent laws #2

Quote:

Originally Posted by

**ford2008** Hi guys,

the task: Simplify using the exponent laws. Write the final answer using only positive exponents. Evaluate where possible.

1. 2x^-1

my answer:

2

---

x

Is that right?

2. (5p^3)^-2

my answer:

1

-----

(5p^3)^2

= 1

-------

10p^6

No, it is not. 5^2= 25, not 10.

Quote:

Is that right?

3. (-32x^-10 y^15)^1/5

my answer:

(-32)^1/5 (x^-10)^1/5 (y^15)^1/5

How can I simplify further???

Why not use the laws of exponents as you did before? (x^-10)^1/5= x^(-10/5) and (y^15)^(1/5)= y^(15/5). And you should be able to calculate that (-2)^2= 4, (-2)^3= (4)(-2)= -8, (-2)^4= (-8)(-2)= 16, and (-2)^5= (16)(-2)= -32.

Quote:

4. ( x^1/2 ) ^1/2

(------------)

(x^1/3 x^1/5)

the whole task is in one bracket and ^1/2 is outside the bracket.

How can I simplify?

Again, use the "laws of exponents": x^a x^b= x^(a+b), (x^a/x^b)= x^(a- b), and (x^a)^b= x^(ab). For example the denominator is x^(1/3)x^(1/5)= x^(1/3+ 1/5). What is 1/3+ 1/5?

Re: Simplify using the exponent laws #2

So the answer for 3 should be = -2^5 x^-10/5 y^3 or not? I am just confused because I have to write the final answer using only positive exponents. But the x exponent is still negative or not?

Task 4 = 1/3 + 1/5 is 5/15 + 3/15 = 8/15.

Re: Simplify using the exponent laws #2

Quote:

Originally Posted by

**ford2008** So the answer for 3 should be = -2^5 x^-10/5 y^3 **<--- nearly!** or not? I am just confused because I have to write the final answer using only positive exponents. But the x exponent is still negative or not?

Task 4 = 1/3 + 1/5 is 5/15 + 3/15 = 8/15.

At #3:

$\displaystyle \left(-32 \cdot x^{-10} \cdot y^{15} \right)^\frac15 = \left(-2^5 \cdot x^{-10} \cdot y^{15} \right)^\frac15 = -2^{5\cdot \frac15} \cdot x^{-10\cdot \frac15} \cdot y^{15\cdot \frac15} $

Now simplify. (btw: -10/5 = -2)